Baltic Astronomy, vol. 12, 221–242, 2003. ATMOSPHERIC EXTINCTION CORRECTIONS FOR WET OBSERVATIONS E. Pakˇstien˙e1 and J.-E. Solheim2 1 Institute of Theoretical Physics and Astronomy, Vilnius University, Goˇstauto 12, Vilnius LT-2600, Lithuania 2 Institutt for Fyzikk, Universitat Tromsø, N-9037, Tromsø, Norway, present: Wilh Wilhelmsen vei 71, N-1362 Hosle, Norway Received December 2, 2002, revised January 13, 2003 Abstract. Account of the extinction in the Earth’s atmosphere is an important part of the WET light curve reduction procedures. Usually, WET observations are not corrected for the second order extinction effects: the dependence of the extinction coefficient on spectral type and on air mass (the Forbes effect). The ignorance of these effects does not change seriously the derived pulsation amplitudes at the frequencies higher than 200 μHz but the increase of the noise at lower frequencies takes place. For obtaining the true extra-atmospheric magnitudes of stars, a modification of the extinction correction procedure is proposed. For photometry with the R647 phototube we recommend to use a filter cutting out the region below 310 nm, in order to decrease and stabilize the extinction coefficient. A method for estimation of spectral type of the comparison star from WET observations is proposed. Key words: methods: data analysis – atmospheric effects – tech- niques: photometric: WET 1. INTRODUCTION Atmospheric extinction is a phenomenon which takes place in the Earth’s atmosphere. Due to extinction the observed stars seem fainter and redder than they are in reality. The amount of the ex- tinction in heterochromatic photometry is different for various types of stars even in the case when they are observed at the same zenith distance (air mass) because of the second order extinction effects. The Forbes effect, which will be explained below, is also significant, especially at large zenith distances, and it can give additional errors in stellar parameters. These effects are especially significant when 222 E. Pakˇstien˙e, J.-E. Solheim super-broad photometric passbands are used in observations (as in WET observations, with no filter). However, in the standard WET reduction procedure, the sec- ond order extinction effect and the Forbes effect are not taken into account. This means that the WET data reduced by the standard programs cannot be used to obtain the true extra-atmospheric mag- nitudes of the investigated stars. For a precise atmospheric extinc- tion correction we have to consider the characteristics and nature of the atmospheric extinction. 2. THE NATURE OF ATMOSPHERIC EXTINCTION AND MONOCHROMATIC EXTINCTION COEFFICIENTS Atmospheric extinction in the Earth’s atmosphere is quite vari- able, usually it changes even during a night. These changes are dependent on the site and on the light wavelength. There are three main sources of the extinction in the atmosphere: (1) The Rayleigh scattering of light by molecules with diameters smaller than the wavelength of the scattered light. The Rayleigh extinction αR(λ, h) in magnitudes at zenith can be calculated by the equation (Hayes & Latham 1975): −4 2 − h αR(λ, h)=0.0094977 · λ · ns(λ) · e 7.996 ,(1) where λ is the wavelength in μm, h is the altitude of the observatory above sea level in km and ns(λ) is the refraction index: 107.6 0.93161 ns(λ)=0.23465 + 146−λ−2 + 41−λ−2 .(2) (2) The ozone extinction αoz(λ) can be calculated from αoz(λ)=1.09 · T · k(λ),(3) where T is the total thickness of the ozone layer at the standard temperature 0◦C and pressure (1 atm) above the observatory, k(λ) is the ozone absorption coefficient. We took its values from the Handbook of Geophysics (1965). (3) The aerosol extinction by scattering and absorption by par- ticles with diameters of the order of the wavelength or larger. The wavelength dependence of the aerosol extinction can be represented by the empirical equation: −b αaer(λ)=A · λ (4) where: αaer(λ) is the aerosol extinction in magnitudes at zenith for a given wavelength λ in μm, A is the same extinction for λ =1μm and b is a coefficient dependent on the size of aerosol particles and their size distribution (Forbes et al. 1996, Pakˇstien˙e 2001) . Atmospheric extinction correction for WET observations 223 The aerosol extinction can be subdivided into two parts: (1) the neutral aerosol extinction αn which does not depend on the wave- length and (2) the selective aerosol extinction αs described by Equa- tion (4). The combined aerosol extinction coefficient can be written as: −bs αaer(λ)=αn + As · λ .(5) A method for determination of the aerosol extinction parameters are has been described in some of our earlier papers (Zdanaviˇcius & Pakˇstien˙e 1997, Pakˇstien˙e et al. 2001). We have determined that the dependence of aerosol extinction on wavelength in many cases is different in the ’blue’ and ’red’ spectral regions. This dependence changes its character at λ ≈ 465 nm. In rare cases, even in such places as the Mol˙etai Observatory (Lithuania) or Mt. Maidanak Observatory (Uzbekistan), the aerosol extinction can be assumed equal to zero (the atmosphere is almost aerosol-free). Figure 1 shows how all the components of the atmospheric extinction depend on the wave- length. Here the atmospheric ex- tinction at zenith is calculated using the atmospheric extinc- tion parameters typical for the Mol˙etai Observatory (h = 220 m, T = 3 mm, αn =0and the mean weighted values of bs Fig. 1. Dependence of the mono- chromatic extinction coefficients on and As are 1.35 and 0.14, respec- wavelength for different atmospheric tively) (Zdanaviˇcius & Pakˇstien˙e extinction components. Atmosphe- 1997). Figure 1 shows that ric extinction at zenith is calculated the Rayleigh extinction and the using the typical atmospheric extinc- ozone absorption are most selec- tion parameters for the Mol˙etai Ob- tive. The ozone absorption influ- servatory (see the text). ences the radiation in the Hug- gins (ultraviolet) and Chappuis (red) bands. The dependence of the Rayleigh extinction on the wavelength is steep in the ultraviolet and becomes flatter at longer wavelengths. The aerosol extinction decreases slowly with increasing wavelength. 3. DESCRIPTION OF THE AEROSOL EXTINCTION The aerosol extinction is the most variable and problematic. It depends on the nature, size and the size distribution of aerosol parti- 224 E. Pakˇstien˙e, J.-E. Solheim cles, which again depend on the location of the observatory and the prevailing winds from the sources of aerosol particles. Aerosols can be formed by the water and solution drops, dust, pollen and soot. All these particles can be of different sizes and can have different distributions by sizes. During a particular night the condensation of water vapor can take place, and the dust can be transported by wind, which change the aerosol types and sizes. With increase of the number of small aerosol particles, the dependence of the aerosol extinction on wavelength becomes stronger, and the selective aerosol extinction increases. The amplitude of the selective aerosol extinc- tion in most cases in smaller than of the neutral extinction (Pakˇstien˙e 2001). The most common sources of the variable neutral extinction are thin clouds. When observations are carried out through clouds, and the two- or three-channel photometers are used for continuous photometry, the Channel 1 counts are being divided by the Channel 2 counts for removal of the cloud effects. However, in this case the final light curve is obtained with somewhat larger scatter of points than in the case when the sky is absolutely clear. This happens because we add the noise from two stars, instead of only one; the effect is even more significant, if Channel 2 contains a fainter star than Channel 1, which is often the case. Neutrally scattering aerosol particles make the stars fainter and the sky brighter. Especially strong brightening of the sky takes place during observations with the Moon or if a bright star is close to the program star. In the case of clouds, the sky subtraction is compli- cated, but this is not the result of atmospheric extinction although the effect is caused by the same particles. Onemoreremarkabouttheskysubtraction:theratioofthe sky values between different channels can vary with time even dur- ing one night. This can be caused by additional lights and their position with respect to the telescope tube. Additional lights can be the daybreak or evening-glow, moonlight, city lights, auroras, etc. These additional light sources can be reflected by the telescope parts or the dome. The dependence of the ratio of the sky values on the telescope position can be investigated by observing the sky in differ- ent directions during several adjacent nights with the moonlight or some glows. Also some photometers record the sky values in a fixed direction relative to the main target, as is the case for Channel 3 in the standard WET photometer (Kleinman et al. 1995) and in the Vilnius design classical WET photometer (Aliˇsauskas et al. 2000). Atmospheric extinction correction for WET observations 225 4. THE SYNTHETIC HETEROCHROMATIC EXTINCTION COEFFICIENTS The synthetic extinction coefficients of a heterochromatic pho- tometric system are calculated by the integral equation: F x − · p (λ)·τ (λ)·I(λ)·ϕ(λ)·dλ α = 2.5 log τ x(λ)·I(λ)·ϕ(λ)·dλ ,(6) where p(λ) is the atmospheric transmittance, F is the air-mass of the Earth’s atmosphere, τ(λ) is the transmittance of interstellar matter, x is the number of the mass units of interstellar matter, I(λ) is the energy distribution in the spectrum of the observed star, ϕ(λ) is the response function of the photometric system. Transmittance of the unit mass of interstellar matter τ(λ) is taken from Straiˇzys (1992), energy distribution in the spectra of stars of various spectral types I(λ) are from Straiˇzys & Sviderskien˙e (1972) and Sviderskien˙e (1980), with extrapolation to UV by Sviderskien˙e (1988).